Hotmath Practice Problems

Section 4-5

Systems of Linear Inequalities

One linear inequality in two variables divides the plane into two half-planes. A system of two or more linear inequalities can divide the plane into more complex shapes.

Example:

Graph the system of linear inequalities.

Graphing the three lines and shading the region enclosed, we get the figure below.

Problem: 1

Find a system of linear inequalities that will define the shaded region.

Problem: 3

Find a system of linear inequalities that will define the shaded region.

Problem: 5

Find a system of linear inequalities that will define the shaded region.

Problem: 7

Find a system of linear inequalities that will define the shaded region.

Problem: 9

Find a system of linear inequalities that will define the shaded region.

Problem: 11

Graph the given linear system.

y –3

y 6 – 3x

Problem: 13

Graph the given linear system.

y 3x – 2

y –x + 3

Problem: 15

Graph the given linear system.

x – 4y 20

x – 5y 20

Problem: 17

Graph the given linear system.

x 5

3y 2

3x + y 6

Problem: 19

Graph the given linear system.

x 0

y 0

x 4

Problem: 21

Graph the given linear system.

x – 2y 5

5x + 2y 3

x + y 4

Problem: 23

Graph the given linear system.

x 0

y 0

x 3

y 3

Problem: 25

Graph the given linear system.

x + y 4

x 1

y 0

Problem: 27

Graph the given linear system.

x 6

x – 3y 2

2x + 3y 8

x + y 7

Problem: 29

Graph the system of inequalities, and find the vertices.

x + y 10

3x – 4y 24

x 0

y 0

Problem: 31

Write a system of linear inequalities that defines a rectangle with vertices at

(3, 2) (4, 2) (4, 5) (3, 5)

Problem: 33

Write a system of linear inequalities that defines a triangle with vertices at (–3, 0), (3, 0) and (0, 3).

Problem: 35

Write a system of linear inequalities that defines a triangle with vertices at (0, 0), (–5, 0) and (–2, 5).

Problem: 37

A club is selling hats and jackets as a fundraiser. They have to stay within a budget of $900. They can order up to 200 items. They must buy at least as many hats as they buy jackets. Each hat costs $3 and each ribbon costs $4.

a) Write a system of inequalities to represent the situation.

b) Graph the inequalities.

c) If the club buys 150 hats and 100 jackets, will the conditions be satisfied?